zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Exact periodic solutions of the complex Ginzburg-Landau equation. (English) Zbl 0943.35087
Summary: Three new exact periodic solutions of the complex Ginzburg-Landau equation are obtained in terms of the Weierstrass elliptic function $\wp$. Furthermore, the new periodic solutions and other shock solutions appear as their bounded limits (along the real axis) for particular relationships between the coefficients in the equation. In the general case, bounded limits are nothing but the already known pulse, hole, and shock solutions. It is also shown that the shapes of the solutions are quite different from the shape of the usual envelope wave solution. In particular, the spatial structure of the new bounded periodic solutions varies in time, while the pulse solution may exhibit breather-like behavior.

35Q55NLS-like (nonlinear Schrödinger) equations
35B10Periodic solutions of PDE
35C05Solutions of PDE in closed form
Full Text: DOI